论文标题
月光，超符号对称性和量子误差校正
Moonshine, Superconformal Symmetry, and Quantum Error Correction
论文作者
论文摘要
特殊的保形场理论可以具有对称群，这是有趣的零星有限简单组。著名的例子包括$ C = 24 $ $ c = 24美元的二维形式形式田野理论（CFT），由Frenkel，Lepowsky和Meurman构建，以及由Duncan和Mack-Crane详细探讨的$ C = 12 $ CFT的Conway对称组。 K3椭圆形属与Mathieu组$ m_ {24} $之间的Mathieu Maonshine连接导致研究了具有大对称组的K3 Sigma模型。 Gaberdiel，Taormina，Volpato和Wendland研究了一个特定的K3 CFT，其中具有最大对称性组，该组合$（4,4）$ Super -Conformal Symmetry在精美的作品中进行了研究。本文表明，在GTVW和$ C = 12 $理论中，可以通过量子误差校正代码理论来理解超符号发生器的构建。这些代码的自动形态组将保留超符号发电机的CFT中的对称组提升。对于GTVW模型的$ n = 1 $超电流，我们的结果加上T. johnson-freyd的结果，意味着对称组是$ M_ {24} $的最大亚组，称为SEXTET组。 （Sextet组也被称为六角形的Holomorph。）在\ cite {gtvw}上构建GTVW模型的Ramond-ramond扇区与奇迹八发生成器有关，进而导致Golay代码作为RR状态的Symmetries symmeties symmetries symmetries。此外，$（4,1）$超符号对称性足以将K3 Sigma模型的椭圆属分解为$ n = 4 $ supercongrongra的字符。保留$（4,1）$的对称组大于保留$（4,4）$的对称组。
Special conformal field theories can have symmetry groups which are interesting sporadic finite simple groups. Famous examples include the Monster symmetry group of a $c=24$ two-dimensional conformal field theory (CFT) constructed by Frenkel, Lepowsky and Meurman, and the Conway symmetry group of a $c=12$ CFT explored in detail by Duncan and Mack-Crane. The Mathieu moonshine connection between the K3 elliptic genus and the Mathieu group $M_{24}$ has led to the study of K3 sigma models with large symmetry groups. A particular K3 CFT with a maximal symmetry group preserving $(4,4)$ superconformal symmetry was studied in beautiful work by Gaberdiel, Taormina, Volpato, and Wendland. The present paper shows that in both the GTVW and $c=12$ theories the construction of superconformal generators can be understood via the theory of quantum error correcting codes. The automorphism groups of these codes lift to symmetry groups in the CFT preserving the superconformal generators. In the case of the $N=1$ supercurrent of the GTVW model our result, combined with a result of T. Johnson-Freyd implies the symmetry group is the maximal subgroup of $M_{24}$ known as the sextet group. (The sextet group is also known as the holomorph of the hexacode.) Building on \cite{gtvw} the Ramond-Ramond sector of the GTVW model is related to the Miracle Octad Generator which in turn leads to a role for the Golay code as a group of symmetries of RR states. Moreover, $(4,1)$ superconformal symmetry suffices to define and decompose the elliptic genus of a K3 sigma model into characters of the $N=4$ superconformal algebra. The symmetry group preserving $(4,1)$ is larger than that preserving $(4,4)$.
